Problem 2: It is recommended to change the circular cross section shown in the figure by a square section carries the same maximum shear stress, suggest the dimensions of the square cross section.
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- Calculate the distance e from the cent crime of the web of a C 15 x 40 channel section to the shear center 5 (see figure). Note: For purposes of analysis, consider the flanges to be rectangles with thickness teequal to the average flange thickness given in Table F-3(a) in Appendix F.A U-shaped cross section of constant thickness is shown in the figure. Derive the following formula for the distance e from the center of the semicircle to the shear center. Also, plot a graph showing how the distance e (expressed as the non dimensional ratio e/r varies as a function of the ratio b/r. (Let b/r range from 0 to 2.)Calculate the distance e from the centerline of the web of a C 310 × 45 channel section to the shear center E (see figure). Note: For put poses of analysis, consider the flanges to be rectangles with thickness îrequal to the average flange thickness given in Table F-3(b) in Appendix F.
- The cross section of a slit square tube of constant thickness is shown in the figure. Derive the following formula for the distance e from the corner of the cross section to the shear center S: e=b22A cross section in the shape of a circular arc of constant thickness is shown in the figure. Derive the following formula for the distance e from the center of the arc to the shear center S: in which ß is in radians. Also, plot a graph showing how the distance e varies as ß varies from 0 to tlA steel plate (called a cover ploie) having cross-sectional dimensions 6,0 in. × 0.5 in. is welded along the full length of the bottom flange of a W 12 × 50 wide-flange beam (sec figure, which shows the beam cross section). What is the percent increase in the smaller section modulus (as compared to the wide-flange beam alone)?
- -15 A composite beam is constructed froma wood beam (3 in. x 6 in.) and a steel plate (3 in, wide). The wood and the steel are securely fastened to act as a single beam. The beam is subjected to a positive bending moment M. = 75 kip-in. Calculate the required thickness of the steel plate based on the following limit states: Allowable compressive stress in the wood = 2 ksi Allowable tensile stress in the wood = 2 ksi Allowable tensile stress in the steel plate = 16 ksi Assume that Ew= 1,500 ksi and es= 30,000 ksi.A square tube section has side dimension of 20 in. arid thickness of 0.5 in. If the section is used for a 10-ft-long beam subjected to 1250 kip-in, torque at both ends, calculate the maximum shear stress and the angle of twist between the ends. Use G = 11,600 ksi.During construction of a highway bridge, the main girders are cantilevered outward from one pier toward the next (see figure). Each girder has a cantilever length of 48 m and an I-shaped cross section with dimensions shown in the figure. The load on each girder (during construction) is assumed to be 9,5 kN/m, which includes the weight of the girder. Determine the maximum bending stress in a girder due to this load.
- The cross section of a slit rectangular tube of constant thickness is shown in the figures. (a) Derive the following formula for the distance e from the centerline of the wall of the tube in the figure part a to the shear center S: (b) Find an expression for e if flanges with the same thickness as that of the tube arc added as shown in figure part b.A beam having a cross section in the form of an un symmetric wide-flange shape (sec figure) is subjected to a negative bending moment acting about the 2 axis. Determine the width b of the top flange in order that the stresses at the top and bottom of the beam will be in the ratio 4:3, respectively.The cross section of a narrow-gage railway bridge is shown in part a of the figure. The bridge is constructed with longitudinal steel grinders that support the wood cross ties. The bridge is constructed with longitudinal steel girders that support the wood cross ties. The girders are restrained against lateral buckling by diagonal bracing, as indicated by the dashed lines. The spacing of the girders is S1= 50 in. and the spacing of the rails is s2= 30 in. The load transmitted by each rail to a single tie is P = 1500 1b. The cross section of a tie, shown in part b of the figure, has a width b =5.0 in. and depth d. Determine the minimum value of d based upon an allowable bending stress of 1125 psi in the wood tie. (Disregard the weight of the tie itself.)